Analytical (“mathematical”) modeling of the dynamic response of a printed circuit board (PCB) to an impact load

Based on the developed analytical (“mathematical”) stress model, we evaluate the dynamic response of a “flexible-and-heavy” square simply supported printed circuit board (PCB) to an impact load applied to its support contour during drop tests. The analysis is restricted to the first mode of vibrations and is carried out in application to a PCB structure employed in an advanced accelerated test setup (test vehicle). The vehicle is aimed at the assessment of the performance, in accelerated test conditions on the board level, of packaging materials (and, first of all, BGA solder joint interconnections) experiencing dynamic (drop or shock) loading. Heavy masses are sometime attached to the PCB to accelerate its dynamic response. These masses are usually small in size, so that while changing the total mass of the board and generating significant inertia forces, they do not affect the board's flexural rigidity, nor its response to the in-plane loading. Such a loading is due to the fact that the PCB's contour is non-deformable, and if the drop height and/or the inertia forces are significant, elevated in-plane (“membrane”) stresses arise in the PCB. As a result of that, a non-linear response of the board to the impact load takes place: the relationship between the magnitude of the dynamic load and the PCB deflections becomes essentially non-linear (with a rigid cubic characteristic of the restoring force). The carried out numerical example, although reflects the characteristics of the PCB and loading conditions in an actual experimental setup, should be viewed merely as an illustration to the general concept. This example demonstrates the attributes and the effectiveness of the suggested method. Analytical and FEA predictions are in good agreement. The developed model is helpful in understanding the physics of the problem. It can be used, along with FEA simulations, in the analysis, structural (“physical”) design and accelerated test efforts of electronic systems of the type in question. The obtained results can be easily generalized, if necessary, for PCB's of different aspect ratios and with other boundary conditions, for different distributions of the added masses, etc., and applied, with adequate modifications, to PCB's in actual use conditions as well.